my lens no longer fits snugly to my camera body, it used to, but now I can turn the lens on the camera some even when it is locked in
That’s very likely your problem right there! To quote that article…
The end result is the discovery that on high resolution cameras, with high-quality wide-angle lens (because side to side variation is much more apparent with a wide angle lens) a very small difference in alignment between the lens mount and the sensor will cause this kind of problem.
How small of a variation? One of his sources said as little as 20 microns (0.02mm or 0.0008 inches) is sufficient to cause side to side variation. You can only detect that amount of variation with laboratory grade laser equipment, I’m told. Medical-grade machine parts (used in arthroscopes, etc.) are expected to have tolerances of about 50 microns, (3) and it would seem unlikely that a camera lens mount would be made more than twice as accurately as a medical arthroscope. In other words, with a top quality wide-angle lens on a high resolution sensor, we can perceive a 20 micron difference, but the manufacturer probably can’t make the part more accurately than +/- 50 microns at a reasonable cost.
Of course, this is talking about wide-angle lenses, but the same principles apply. If it turns far enough in the mount, maybe the electrical contacts aren’t even lining up properly, thereby causing the AF to malfunction!
Is it loose on another camera body, or is it just on your own? I know the T3 is very cheap and plasticky, so the weight of that large lens may have “broken” the mount.